Archive Panic:
    It can be a bit daunting figuring out how to get into Richard D. James' music, considering all of the aliases and styles of music present. Many (including this flowchart◊) suggest to start with 1992's Selected Ambient Works 85-92, then branch to Richard d. James album and SYRO (all released under the Aphex Twin name), and finding what one likes from there.
    This trope occurred again when James started up his SoundCloud page, uploading 200+ songs spanning his entire career, and making nearly all of it freely downloadable. 
Creepy Awesome: "Come to Daddy", and its video.
Ear Worm:
    "Donkey Rhubarb." Click at your own risk.
    "Digeridoo", likewise.
    Pretty much all of Syro, but "Minipops 67" and "CIRCLONT6A" stand out. 
Fandom Rivalry: With the fandom of Skrillex. Odd, because Skrillex himself is a HUGE fan of Aphex Twin, so much so that he declared him as his main influence. Becomes even more odd if you consider that Aphex openly stated he doesn't know much of Skrillex to give an opinion of him, but also said that he respects the more mainstream electronic music artists, finding them as a gateway to electronic music in general.
First Installment Wins: Selected Ambient Works 85-92 is considered one of the greatest electronic music albums ever recorded.
Hell Is That Noise:
    "Ventolin", which combines a piercing tone with crunching and discordant beats. The tone was described by James as what one hears when overdosing on Ventolin, aka Salbutamol, an asthma medication infamously known for having tinnitus as a side effect.
    The remix of "We Have Arrived" that he provided for Mescalinum United. They and "Ventolin" are the most migraine-inducing pieces in James' career.
    The robotic voice in "Come to Daddy" chanting about how much they're craving your soul. Special mention goes to that scream. 
Memetic Mutation:
    Variations of the titles of his first two albums have seen widespread homage, especially from ambient artists.
    COME TO DADDY!
    His infamous grin has been used/shopped quite a few times. 
Misattributed Song:
    Subverted with Pac-Man, which he released under the alias "Power Pill".
    Averted with being credited to making a Tetris remix.
    A handful of songs on P2P networks from the early 2000s were generally attributed to him. One of the most famous ones, "outside (kick ass violin solo)", is actually a song by Outside called "To Forgive But Not Forget (Lim'chol V'lo Lishkoach)". 
Most Wonderful Sound:
    A lot of his ambient tracks, especially those found on Selected Ambient Works Volume II. "[rhubarb]" is a shining example of this.
    When the distorted bass comes in at the end of "Windowlicker".
    For some, the "Come to Daddy" scream might even be this. 
Narm: While "Come To Daddy" is still an awesome song, some of the lyrics are a bit over-the-top. "I WILL EAT YOUR SOOOOUUUUL!!!"
Seinfeld Is Unfunny: One may listen to Selected Ambient Works 85-92 and find nothing particularly special about it, not taking into account that the sounds on this album were revolutionary and never before heard when it came out in 1992. (It's still unclear whether the dates in the title are truthful considering James' history with the press, but if true, actually rewrite the history of electronic music.) Aiding this trope along is that, over 20 years later, the album does sound a bit dated.
Signature Song: "Come to Daddy" and "Windowlicker" are his two greatest commercial hits, although songs like "Avril 14th" and "Flim" are deemed by fans to be some of his best works.
Song Association:
    Most racing game fans would associate "Come To Daddy" with Project Gotham Racing 3 and Motorstorm Pacific Rift.
    Of course, "Windowlicker" is in Grand Theft Auto V. 
Sweet Dreams Fuel:
    Selected Ambient Works 85-92 and Selected Ambient Works Volume II are full of these - see the trope page.
    To say nothing of "Flim" and "Avril 14th."
    "Goon Gumpas" and "Logan Rock Witch" both sound like something that would fit extremely well on a Disney soundtrack.
    "IZ-US" is a pretty relaxing song if you don't mind a little percussion.
    The sections of "Girl/Boy Song" that don't have the erratic percussion. It's actually a very beautiful orchestral song that wouldn't sound too out-of-place in a cartoon and is even accompanied by a xylophone riff near the end of the song.
    "Piano Un10 It Happened"
    "Aisatsana", the closing track to Syro. It even includes birds chirping and other nature sounds for maximum relaxation! 
Tear Jerker:
    "Avril 14th" and jynweythek, with both being desolate piano pieces on Drukqs.
    "Rhubarb" and "Stone in Focus", with both being ambient SAW Vol II pieces.
    "Nannou", a song dedicated to his girlfriend composed wholly from music box samples.
    Richard made the Aphex Twin name as a memorial of sorts to his older brother, also named Richard, who died at birth. The Girl/Boy EP cover is a picture of his grave decorated with flowers. And likewise, "Girl/Boy Song" is a pretty heavy listen despite being a thematically and aesthetically whimsical track.
    The utter Sweet Dreams Fuel that is "Flim" and "Fingerbib".
    "Piano Un10 It Happened"